The vectors `2 hat(i) + 2 hat(j) + 4 hat(k) and 6 hat(i)` represent the two sides of a triangle . Find the following .
a vector perpendicular to the plane of the triangle .

Explanation

To find a vector that is perpendicular to the plane of the triangle formed by the vectors \( \mathbf{AB} = 2\hat{i} + 2\hat{j} + 4\hat{k} \) and \( \mathbf{AC} = 6\hat{i} \), we can use the cross product of these two vectors. The cross product of two vectors results in a vector that is perpendicular to both of the original vectors.

### Step-by-Step Solution:

1. **Identify the Vectors**:
- Let \( \mathbf{AB} = 2\hat{i} + 2\hat{j} + 4\hat{k} \)
- Let \( \mathbf{AC} = 6\hat{i} \)

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